Gabriela is 2 times as old as Ben. 36 years ago, Gabriela was 8 times as old as Ben. How old is Ben now?
Solution: We can use the given information to write down two equations that describe the ages of Gabriela and Ben. Let Gabriela's current age be $g$ and Ben's current age be $b$ The information in the first sentence can be expressed in the following equation: $g = 2b$ 36 years ago, Gabriela was $g - 36$ years old, and Ben was $b - 36$ years old. The information in the second sentence can be expressed in the following equation: $g - 36 = 8(b - 36)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $b$ , it might be easiest to use our first equation for $g$ and substitute it into our second equation. Our first equation is: $g = 2b$ . Substituting this into our second equation, we get: $2b$ $-$ $36 = 8(b - 36)$ which combines the information about $b$ from both of our original equations. Simplifying the right side of this equation, we get: $2 b - 36 = 8 b - 288$ Solving for $b$ , we get: $6 b = 252.$ $b = 42$.